Pith Number

pith:U6U5HCQK

pith:2011:U6U5HCQKBP45V6OYY7AFDP7NYF

not attested not anchored not stored refs pending

Singular curves over a finite field and with many points

E. Ballico

arxiv:1109.2223 v3 · 2011-09-10 · math.AG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{U6U5HCQKBP45V6OYY7AFDP7NYF}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T02:54:28.178120Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a7a9d38a0a0bf9daf9d8c7c051bfedc153c0ba2670b6308cf4ad16b0e8255f25

Aliases

arxiv: 1109.2223 · arxiv_version: 1109.2223v3 · doi: 10.48550/arxiv.1109.2223 · pith_short_12: U6U5HCQKBP45 · pith_short_16: U6U5HCQKBP45V6OY · pith_short_8: U6U5HCQK

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/U6U5HCQKBP45V6OYY7AFDP7NYF \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: a7a9d38a0a0bf9daf9d8c7c051bfedc153c0ba2670b6308cf4ad16b0e8255f25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f8070e4a1cfca41afbe4cbb5a7bb349425b7f3fd33358155b349fc0a738db823",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-09-10T13:59:37Z",
    "title_canon_sha256": "e6db0c32a4e4df7cd71fb4ad59746d1ae7d79ccb9ee1a64bac83e24aea23dab4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1109.2223",
    "kind": "arxiv",
    "version": 3
  }
}